Question: Reduce to lowest terms: $- \dfrac{5}{3} \div \dfrac{1}{6} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{1}{6}$ is $ \dfrac{6}{1}$ Therefore: $ - \dfrac{5}{3} \div \dfrac{1}{6} = - \dfrac{5}{3} \times \dfrac{6}{1} $ $ \phantom{- \dfrac{5}{3} \times \dfrac{6}{1}} = \dfrac{-5 \times 6}{3 \times 1} $ $ \phantom{- \dfrac{5}{3} \times \dfrac{6}{1}} = \dfrac{-30}{3} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-30}{3} = \dfrac{-30 \div 3}{3 \div 3} = -10 $